On structural contraction of biological interaction networks
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866918344121122816 |
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| author | Al-Radhawi, M. Ali Angeli, David Sontag, Eduardo |
| author_facet | Al-Radhawi, M. Ali Angeli, David Sontag, Eduardo |
| contents | Biological networks are customarily described as structurally robust. This means that they often function extremely well under large forms of perturbations affecting both the concentrations and the kinetic parameters. In order to explain this property, various mathematical notions have been proposed in the literature. In this paper, we propose the notion of structural contractivity, building on the previous work of the authors. That previous work characterized the long-term dynamics of classes of Biological Interaction Networks (BINs), based on "rate-dependent Lyapunov functions". Here, we show that stronger notions of convergence can be established by proving structural contractivity with respect to non-standard polyhedral $\ell_\infty$-norms. In particular, we show that such networks are nonexpansive. With additional verifiable conditions, we show that they are strictly contractive over arbitrary positive compact sets. In addition, we show that such networks entrain to periodic inputs. We illustrate our theory with examples drawn from the modeling of intracellular signaling pathways. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_13678 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On structural contraction of biological interaction networks Al-Radhawi, M. Ali Angeli, David Sontag, Eduardo Optimization and Control Dynamical Systems Molecular Networks 93D05, 80A30, 47H09, 37B25, 05C90, 92B99, 34A34, 34D30, 37C20 Biological networks are customarily described as structurally robust. This means that they often function extremely well under large forms of perturbations affecting both the concentrations and the kinetic parameters. In order to explain this property, various mathematical notions have been proposed in the literature. In this paper, we propose the notion of structural contractivity, building on the previous work of the authors. That previous work characterized the long-term dynamics of classes of Biological Interaction Networks (BINs), based on "rate-dependent Lyapunov functions". Here, we show that stronger notions of convergence can be established by proving structural contractivity with respect to non-standard polyhedral $\ell_\infty$-norms. In particular, we show that such networks are nonexpansive. With additional verifiable conditions, we show that they are strictly contractive over arbitrary positive compact sets. In addition, we show that such networks entrain to periodic inputs. We illustrate our theory with examples drawn from the modeling of intracellular signaling pathways. |
| title | On structural contraction of biological interaction networks |
| topic | Optimization and Control Dynamical Systems Molecular Networks 93D05, 80A30, 47H09, 37B25, 05C90, 92B99, 34A34, 34D30, 37C20 |
| url | https://arxiv.org/abs/2307.13678 |